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If you were to drain the rear end, it would take 1.69 quarts of gear oil & 4 ounces of limited slip additive. Or you can do the easy route, like I did today, & use Amsoil's Severe gear oil 75W-90 weight. This oil needs no additive. The fill plug on the rear end faces the rear of the car & the drain plug is on the bottom. Fill to the bottom edge of the fill hole. I bought a hand pump from Amsoil for like $10. Did the job beautifully in about half an hour. Both plugs get torqued to 26 lbs. Afterwards, do some tight, slow circles in both directions, going forwards & reverse. This will work the gear oil into the clutches in the rear end. good luck!!
What you are experiencing may be differential "chatter"... or it could be something more serious. You can read a little about this on the AMSOIL Slip Lock Additive link below.
As mentioned by allmee above, the AMSOIL Severe Gear 75w90 mentioned above already includes the friction modifier though they do sell the modifier for situations such as yours, if you chose to add modifier to your existing fluid vice changing out the fluid.